CUET 2024 Maths Chapter 4 - Determinants MCQs

Maths Chapter 4 – Determinants MCQ Question Answers for CUET 2024

1. Which of the following conditions holds true for a system of equations to be consistent?

a.It should have exactly two solutions

b.It should have no solutions

c.It should have exactly one solution

d.It should have one or more solutions

2. Question

a.an infinite set

b.an empty set

c.a singleton

d.a finite set containing two or more elements

3. System of equations AX = B is inconsistent if

a.(adj A) B ≠ 0

b.(adj A) B = 0

c.│A│ ≠ 0

d.│B│ = 0

4. For a given system of equations if |A|=0 and (adj A)B≠O(zero matrix), then which of the following is correct regarding the solutions of the given equations?

a.the solution does not exist

b.there are one or more solutions

c.there will be exactly one solution

d.there will be exactly two solutions

5. Question

a.Exactly one value of λ

b.Exactly three values of λ

c.Exactly four values of λ

d.Exactly two values of λ

6. Question

a.c

b.d

c.a

d.b

7. If A is any square matrix of order 3 x 3 such that |a| = 3, then the value of |adj. A| is?

a.13

b.3

c.9

d.27

8. Solve the following system of equations x – y + z = 4, x – 2y + 2z = 9 and 2x + y + 3z = 1.

a.x = 2, y = 4, z = 6

b.x = -1, y = -3, z = 2

c.x = -4, y = -3, z = 2

d.x = 3, y = 6, z = 9

9. If the points (2, -3), (k, -1) and (0, 4) are collinear, then find the value of 4k.

a.7/140

b.40/7

c.4/7

d.4

10. If the area of the triangle is 35 sq. units with vertices (2, -6), (5, 4) and (k, 4). Then k is

a.12

b.-2

c.12, -2

d.-12, -2

11. Find the area of the triangle with vertices P(4, 5), Q(4, -2) and R(-6, 2).

a.35 sq. units

b.30 sq. units

c.21 sq. units

d.40 sq. units

12. We can add two matrices having real numbers A and B if their

a.elements are same

b.rows are same

c.columns are same

d.order is same

13. If the points (2, -3), (k, -1) and (0, 4) are collinear, then find the value of 4k.

a.47

b.7/140

c.40/7

d.4

14. Question

a.1

b.2

c.-2

d.-1

15. A system of linear equations AX = B is said to be inconsistent, if the system of equations has

a.No Solution

b.Unique Solutions

c.Trivial Solution

d.Infinite Solutions

16. If A is a square matrix of order 3 and |A| = 5 then |3A| = ?

a.15

b.32

c.45

d.135

17. If 4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1, then z = …………….

a.3

b.2

c.-2

d.1

18. If A is an invertible matrix of order 2, then det (A–1) is equal to

a.0

b.det (A)

c.1

d.1/det (A)

19. Given that A is a square matrix of order 3 and |A| = -4, then |adj A| is equal to

a.-4

b.4

c.16

d.-16

20. Find the area of the triangle whose vertices are (-2, 6), (3, -6) and (1, 5).

a.30 sq. units

b.35 sq. units

c.15.5 sq. units

d.40 sq. units

21. Question

a.I

b.O

c.A

d.None of these

22. Using determinants, find the equation of the line joining the points (1, 2) and (3, 6).

a.y = x

b.x = 3y

c.y = 2x

d.4x – y = 5

23. If A is a square matrix of order 3 and |A| = 7 then |AT| =

a.1/7

b.7

c.21

d.3

24. If A is a symmetric matrix, then At =

a.12:00 AM

b.Diagonal matrix

c. |A|

d.A

25. A non-trivial solution of the system of equations x + λy + 2z = 0, 2x + λz = 0, 2λx – 2y + 3z = 0 is given by x : y : z =

a.2 : 1 : -2

b.1 : 2 : -2

c.2 : 1 : 2

d.1 : -2 : 2

26. The area of a triangle with vertices (-3, 0) (3, 0) and (0, k) is 9 sq. units. The value of k will be

a.9

b.0

c.-9

d.3

27. If A is a square matrix of order 3 and |A| = 5, then the value of |2A′| is

a.-40

b.-10

c.10

d.40

28. Inverse of a matrix A exists, if

a.Matrix A is non-singular

b.Matrix A is singular

c.AT = A

d.| A | = 0

29. Question

a.c

b.b

c.a

d.d

30. Question

a.c

b.d

c.a

d.b

31. The minor Mij of an element aij of a determinant is defined as the value of the determinant obtained after deleting the

a.ith row of the determinant

b.ith row and jth column of the determinant

c.ith column and jth row of the determinant

d.jth row of the determinant

32. If the system of equations x + ky – z = 0, 3x – ky – z = 0 & x – 3y + z = 0 has non-zero solution, then k is equal to

a.0

b.1

c.-1

d.2

33. Question

a.Zero

b.1

c.3

d.2

34. Question

a.a

b.b

c.c

d.d

35. If the equations 2x + 3y + z = 0, 3x + y – 2z = 0 and ax + 2y – bz = 0 has non-trivial solution, then

a.a – b – 8 = 0

b.a + b = 3

c.a + b + 1 = 0

d.a – b = 2

36. In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has value

a.9

b.1

c.24

d.16

37. Which of the following is correct?

a.Determinant is a square matrix

b.None of these

c.Determinant is a number associated to a matrix

d.Determinant is a number associated to a square matrix

38. The area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 sq. units. The value of ‘k’ will be:

a.9

b.6

c.3

d.-9

39. If the points (3, -2), (x, 2), (8, 8) are collinear, then find the value of x.

a.2

b.4

c.5

d.3

40. The area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 sq. units. The value of k will be

a.6

b.-9

c.9

d.3

41. Question

a.d

b.b

c.a

d.c

Also See :

Maths Ch 1 – Relations and Functions MCQs
Maths Ch 2 – Inverse Trigonometric Functions MCQs
Maths Ch 3 – Matrices MCQs
Maths Ch 5 – Continuity and Differentiability MCQs
Maths Ch 6 – Applications of Derivatives MCQs
Maths Ch 7 – Integrals MCQs
Maths Ch 8 – Application of the Integrals MCQs
Maths Ch 9 – Differential Equations MCQs
Maths Ch 10 – Vectors MCQs
Maths Ch 11 – Three Dimensional Geometry MCQs
Maths Ch 12 – Linear Programming MCQs
Maths Ch 13 – Multiplication Theorem Probability MCQs

CUET 2024 Maths Chapter 4 – Determinants MCQ Question and Answers – MCQs for Practice

Maths Chapter 4 – Determinants MCQ Question Answers for CUET 2024

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